I tried a different monitor and cables, no change. The heatsink is firmly against the motherboard. The video card feels firmly connected, but I can still try to reseat it.
My network lights indicate memory failure. I tried reseating both cards, then using one at a time. With one memory card, the network lights indicate memory failure again, but using the other alone only powers up the computer for a split second with only the "C" network light glowing green (A, B, D are off), then turns off. From this, is it safe to assume my RAM is the problem, or should I continue checking the video card and PSU?